Strictly Proper Decision Markets
A reminder about Problem set 2 • Due in 8 days • Project proposals are due less than a week after • Literature review is an opportunity to get a head start on the proposal and projects
What is a Decision Market? • It’s a lot like a prediction market
Discuss: Why do we speculate? • What are we running prediction markets for?
History: Hanson writes an article
Hanson’s decision markets
Hanson’s decision markets Possible Policies Quantitative Easing Helicopter Money No stimulus Adopting NDGP
Hanson’s decision markets Possible Policies Effect on GDP Quantitative Easing Helicopter Money No stimulus Adopting NDGP
Hanson’s decision markets Possible Policies Effect on GDP Quantitative Easing ? Helicopter Money No stimulus Adopting NDGP
Hanson’s decision markets Possible Policies Effect on GDP Quantitative Easing ? Helicopter Money No stimulus Adopting NDGP
Hanson’s decision markets Possible Policies Effect on GDP Quantitative Easing +.3% Helicopter Money +.9% No stimulus -.8% Adopting NDGP +1.7%
Hanson’s decision markets Possible Policies Effect on GDP Quantitative Easing +.3% Helicopter Money +.9% No stimulus -.8% Adopting NDGP +1.7%
Hanson’s decision markets Possible Policies Effect on GDP Quantitative Easing +.3% (?) Helicopter Money +.9%(+1.5%) No stimulus -.8% (?) Adopting NDGP +1.7% (+1.1%)
Philosophy: Markets with agency Art’s vocation is to unveil the truth in the form of sensuous artistic configuration, to set forth the reconciled opposition just mentioned [the common world of earthly temporality, and a realm of thought and freedom], and so to have its end and aim in itself, in this very setting forth and unveiling. Hegel
Philosophy: Markets with agency If Hegel had written the whole of his logic and then said, in the preface or some other place, that it was merely an experiment in thought in which he had even begged the question in many places, then he would certainly have been the greatest thinker who had ever lived. As it is, he is merely comic. Kierkegaard
Philosophy: Markets with agency You love the accidental. A smile from a pretty girl in an interesting situation, a stolen glance, that is what you are hunting for, that is a motif for your aimless fantasy. You who always pride yourself on being an observateur must, in return, put up with becoming an object of observation. Kierkegaard
Philosophy: Markets with agency And thus the native hue of resolution Is sicklied o'er with the pale cast of thought; And enterprises of great pith and moment, With this regard, their currents turn awry, And lose the name of action. Hamlet
Markets where actions matter • Othman and Sandholm ▫ Single expert decision making • Chen and Kash ▫ Single expert decision making (generally) • Shi, Conitzer, Guo ▫ Principal-aligned scoring rules • Boutilier ▫ Self-interested experts
Modeling Decision Markets • A decision maker considers • A set of possible actions, A ▫ E.g. up, down, invest in project A, hire person B, implement policy X, travel to Istanbul, etc. • A set of outcomes of interest, O ▫ Will we see a profit? Will public welfare increase? Will I eat some kebab? • And wants to learn the mapping from actions (A) to outcomes (O) to make an informed decision
Modeling Decision Markets Step 1: Elicit action-outcome matrices
Discuss: What are other examples? • And what drawbacks / possibilities are there for each one?
Modeling Decision Markets Step 2: Create a decision policy
Modeling Decision Markets Review market’s closing prediction Step 2: Create a decision policy
Modeling Decision Markets Create probability distribution over the actions 80% 20% Review market’s closing prediction decision rule d Step 2: Create a decision policy
Modeling Decision Markets 80% 20% Step 3: Pick an action
Modeling Decision Markets Step 4: Observe the outcome
Modeling Decision Markets Step 5: Score experts
Modeling Decision Markets Actions (Springfield) Action-Outcome matrix Decision policy (.8, .2) Outcomes (Profit) Step 5: Score experts
Modeling Decision Markets decision scoring rule scoring rule
Discuss: why is strict properness important? • Because it totally is.
Strict Properness for an expert
Strict Properness for an expert
Strict Properness for an expert expected score
Strict Properness for an expert expected score
Strict Properness for an expert expected score how likely action a is to be taken given your report p (remember, only one expert so first report is the last report)
Strict Properness for an expert expected score how likely action a is to be taken given your report p (remember, only one expert so first report is the last report)
Strict Properness for an expert expected score your belief in the likelihood of outcome o given action a is taken how likely action a is to be taken given your report p (remember, only one expert so first report is the last report)
Strict Properness for an expert expected score your belief in the likelihood of outcome o given action a is taken how likely action a is to be taken given your report p (remember, only one expert so first report is the last report)
Strict Properness for an expert expected score score for your prediction given this action and outcome your belief in the likelihood of outcome o given action a is taken how likely action a is to be taken given your report p (remember, only one expert so first report is the last report)
Strict Properness for an expert The unique score maximizing prediction is always your true beliefs.
Strict Properness for a market
Discuss: why are markets different? • How many people are in a market? Not one but…
Strict Properness for a market
Strict Properness for a market decision policy now arbitrary
Strict Properness for a market
Strict Properness for a market expected score
Strict Properness for a market expected score
Strict Properness for a market expected score in a prediction market this term is constant in a decision market it depends on d, the decision policy, which depends on…
Strictly Proper Pair
Strictly Proper Pair strict properness for an expert makes prior prediction constant
Strictly Proper Pair
Strict Properness Summary • Different constraints for a single expert and many experts in a market • A strictly proper pair is strictly proper for both • These describe all of strictly proper for a market pairs (minus some uninteresting basically the same set) • But not quite all of strict properness for an expert
Randomly taking any action is necessary
Randomly taking any action is necessary
Randomly taking any action is sufficient
Randomly taking any action is sufficient take a strictly proper scoring rule
Randomly taking any action is sufficient 2. divide by the inverse likelihood the action is taken 1. take a strictly proper scoring rule
Randomly taking any action is sufficient 2. divide by the inverse likelihood the action is taken 3. gives the same expected value as many strictly proper prediction markets 1. take a strictly proper scoring rule
Example 80% 20%
Example expected score using log scoring rule for two prediction markets (2/3 log 2/3 + 1/3 log 1/3) + (2/5 log 2/5 + 3/5 log 3/5)
Example 80% 20% expected score using log scoring rule .8(2/3 log 2/3 + 1/3 log 1/3) + .2(2/5 log 2/5 + 3/5 log 3/5)
Example 80% 20% expected score using ( unbiased ) log scoring rule .8/.8(2/3 log 2/3 + 1/3 log 1/3) + .2/.2(2/5 log 2/5 + 3/5 log 3/5)
Characterization
Discuss: where does this leave us? • Are these markets practical/credible?
Where the first prediction is also the last
Hypothetical • I am a firm and I want to open a store in a city that maximizes my profit. • I will open a store in whatever city you say. • I will pay you 1% of my eventual profit.
Hypothetical • I am a firm and I want to open a store in a city that maximizes my profit. • I will open a store in whatever city you say. • I will pay you 1% of my eventual profit. Right-action rule (RAR)
Research is fun (aside)
Research is fun (aside) (part 2)
Preferences
Preferences Previously we didn’t have to talk about preferences, but it turns out only some preferences have right-action rules!
Preferences
Preferences
Preferences
Preferences
Discuss: single expert v. market • Sometimes one or the other?
Discuss: where do we go from here? • the undiscovere'd country (?)
Conclusion • Decision markets are part of an emerging interest in “markets that do things” • This started as a 286r project ▫ Think big about your project!
Recommend
More recommend
